ERB Framework: A Reconstruction of the Standard Model from a Single Mechanical Postulate
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2026
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| _version_ | 1866902328599117824 |
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| author | Speckmann, Daniel |
| author_facet | Speckmann, Daniel |
| contents | <p>We present the Emergent Resonant Brane (ERB) framework, version 26, a systematic reconstruction program for quantum field theory from a single mechanical postulate: two colliding vacuum branes with mass-density ratio ξ = m_B/m_A = 3/2. This ratio is not chosen to fit data — it is the smallest ratio of two distinct primes, the unique fixed point at which a two-brane system reaches minimum entropy production and maximum resonance stability under the Callan-Symanzik flow.</p> <p>From this single input, a strictly causal five-level chain (L0→L5) with zero upward information flow derives: the coupling constant g = 3/25 = 0.12 (Le Chatelier closure), the penetration scale k as a field eigenvalue (not a fit parameter), the complete CKM matrix (MAE = 6.94×10⁻⁴, zero free parameters in the mixing sector), the Jarlskog invariant J = 2.95×10⁻⁵ (1.69% error vs. PDG), the fine-structure constant α_EM = 1/137.071 (0.025% error, Berry-phase holonomy), and — new in v26 — the pion mass as the Goldstone mode of interface torsion: m_π(dimensionless) = √(ε₀·δ·m_eff)·(1−3θ_B) = 0.1393 (0.18% error vs. PDG).</p> <p>CP violation is proven to be geometric: J = 0 exactly without the sgn(Δr) term in the Whip phase operator, verified in four independent cases. Three fermion generations emerge structurally from the SO(3) Bessel spectrum — not postulated. The quark-lepton mass hierarchy is explained by the gyroscope model: the moment of inertia I_i = m_i·r_i² of the top quark (I ≈ 5737) is 2.7×10⁵ times larger than that of the up quark (I ≈ 0.022), freezing the heavy generation at its topological Bessel radius while light quarks precess freely.</p> <p>The PMNS near-maximal mixing follows as the evanescent limit of the same resonance operator: at the lepton penetration scale k_L = 4k_Q, the wave function spreads across all three Bessel nodes, driving mixing angles toward π/4. The gauge structure U(1)×SU(2)×SU(3) emerges as collective brane oscillations: the photon as a massless phase-gradient wave, the W/Z mass from the 3/2 mechanical mismatch without a Higgs field, and gluons as lattice shear waves with confinement via linear string tension.</p> <p>Wilsonian renormalization is reinterpreted physically: the UV cutoff Λ = 464.1 GeV is the brane collision scale. Running couplings are the elastic substrate's response to different wavelength modes. Renormalization is not a mathematical trick — it is the transition from the discrete ERB substrate to the continuous QFT. The 3/2 attractor is stable by entropy minimisation: any deviation ξ = 3/2 + ε induces phase dissipation at rate dS/dt ∝ ε², forcing the system back to the fixed point.</p> <p>All results, open problems, and derivation gaps are explicitly labelled (PROVEN / DERIVED / CANDIDATE / HYPOTHESIS / OPEN). The primary falsifiable prediction is δ_CP ≈ 352° for leptonic CP violation, testable by the DUNE experiment (~2030). Falsification criterion: |δ_CP(measured) − 352°| > 20°.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19180279 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | ERB Framework: A Reconstruction of the Standard Model from a Single Mechanical Postulate Speckmann, Daniel Emergent gauge symmetry, CKM matrix, CP violation, Jarlskog invariant, U(1) x SU(2) x SU(3), Resonant Brane Model, Flavor Clock, Whip effect, topological modes, quantum field theory, lattice simulation, numerical validation emergent gauge symmetry CKM matrix CP violation Jarlkog invariant quantum field theory Mass Hierarchy Emergent Symmetry Einstein-Field-Theory Bessel Functions Inertial Warping <p>We present the Emergent Resonant Brane (ERB) framework, version 26, a systematic reconstruction program for quantum field theory from a single mechanical postulate: two colliding vacuum branes with mass-density ratio ξ = m_B/m_A = 3/2. This ratio is not chosen to fit data — it is the smallest ratio of two distinct primes, the unique fixed point at which a two-brane system reaches minimum entropy production and maximum resonance stability under the Callan-Symanzik flow.</p> <p>From this single input, a strictly causal five-level chain (L0→L5) with zero upward information flow derives: the coupling constant g = 3/25 = 0.12 (Le Chatelier closure), the penetration scale k as a field eigenvalue (not a fit parameter), the complete CKM matrix (MAE = 6.94×10⁻⁴, zero free parameters in the mixing sector), the Jarlskog invariant J = 2.95×10⁻⁵ (1.69% error vs. PDG), the fine-structure constant α_EM = 1/137.071 (0.025% error, Berry-phase holonomy), and — new in v26 — the pion mass as the Goldstone mode of interface torsion: m_π(dimensionless) = √(ε₀·δ·m_eff)·(1−3θ_B) = 0.1393 (0.18% error vs. PDG).</p> <p>CP violation is proven to be geometric: J = 0 exactly without the sgn(Δr) term in the Whip phase operator, verified in four independent cases. Three fermion generations emerge structurally from the SO(3) Bessel spectrum — not postulated. The quark-lepton mass hierarchy is explained by the gyroscope model: the moment of inertia I_i = m_i·r_i² of the top quark (I ≈ 5737) is 2.7×10⁵ times larger than that of the up quark (I ≈ 0.022), freezing the heavy generation at its topological Bessel radius while light quarks precess freely.</p> <p>The PMNS near-maximal mixing follows as the evanescent limit of the same resonance operator: at the lepton penetration scale k_L = 4k_Q, the wave function spreads across all three Bessel nodes, driving mixing angles toward π/4. The gauge structure U(1)×SU(2)×SU(3) emerges as collective brane oscillations: the photon as a massless phase-gradient wave, the W/Z mass from the 3/2 mechanical mismatch without a Higgs field, and gluons as lattice shear waves with confinement via linear string tension.</p> <p>Wilsonian renormalization is reinterpreted physically: the UV cutoff Λ = 464.1 GeV is the brane collision scale. Running couplings are the elastic substrate's response to different wavelength modes. Renormalization is not a mathematical trick — it is the transition from the discrete ERB substrate to the continuous QFT. The 3/2 attractor is stable by entropy minimisation: any deviation ξ = 3/2 + ε induces phase dissipation at rate dS/dt ∝ ε², forcing the system back to the fixed point.</p> <p>All results, open problems, and derivation gaps are explicitly labelled (PROVEN / DERIVED / CANDIDATE / HYPOTHESIS / OPEN). The primary falsifiable prediction is δ_CP ≈ 352° for leptonic CP violation, testable by the DUNE experiment (~2030). Falsification criterion: |δ_CP(measured) − 352°| > 20°.</p> |
| title | ERB Framework: A Reconstruction of the Standard Model from a Single Mechanical Postulate |
| topic | Emergent gauge symmetry, CKM matrix, CP violation, Jarlskog invariant, U(1) x SU(2) x SU(3), Resonant Brane Model, Flavor Clock, Whip effect, topological modes, quantum field theory, lattice simulation, numerical validation emergent gauge symmetry CKM matrix CP violation Jarlkog invariant quantum field theory Mass Hierarchy Emergent Symmetry Einstein-Field-Theory Bessel Functions Inertial Warping |
| url | https://doi.org/10.5281/zenodo.19180279 |